Adiabatic manipulation Adiabatic manipulation of architectures of multilevel artifjcial atoms of architectures of multilevel artifjcial atoms Giuseppe Falci QUINN – QU antum IN formation & N anostructures GF, E. Paladino, P.G. Di Stefano, A. Ridolfo, A. D'Arrigo Università di Catania Dipartimento di Fisica e Astronomia CNR-IMM UoS Catania Centro Siciliano di Fisica Nucleare e Struttura della Materia Istituto Nazionale di Fisica Nucleare Boris Altshuler’s 60th birthday Boris Altshuler’s 60th birthday Frontiers of Nanoscience, Trieste Aug-Sept 2015 Frontiers of Nanoscience, Trieste Aug-Sept 2015
quantum coherence in the solid state quantum coherence in the solid state a 35 years (very short & personal) roadmap a 35 years (very short & personal) roadmap mesoscopic phenomena in solids “ Quantum mechanical coherence of electron wavefunctions in materials with imperfections has led to major revisions in the theory of electrical conductivity and to novel phenomena in submicron devices.” Altshuler & Lee, Phys Today (1988) quantum bits in a solid state devices Nakamura et al. Nature 398,786 (1999) Frontier of Nanoscience quantum coherent hybrid netwoks J. Fekete, et al. , PRL (2013)
superconducting-based artifjcial atoms superconducting-based artifjcial atoms mesoscopic devices with the functionality of atoms mesoscopic devices with the functionality of atoms why ? With respect to natural atoms they present ● much more fmexible design → several design solutions ● large degree of integration ● on-chip tunability ● stronger couplings → faster processing ● easy signal production and detection ● photons easily confjned in 1D fj fjg. from Xiang et al.RMP 2013 Charge 1999 main design NEC, Chalmers Devoret, solutions Schoelkopf Science 2013 2002 Energy Quantronium CEA Saclay 2000 TU Delft Phase 2002 Flux NIST
artifjcial atoms artifjcial atoms decoherence decoherence Noise is broad band colored low (1/f ) and high-frequency (quantum) Paladino, Galperin, Falci, Altshuler, RMP (2014) Bylander et al., Nat. Phys (2011) Noise sources design dominant source subdominant Cooper pair box charge fmux/phase/circuit fmux fmux crit. current/charge phase crit. curr/impurities dielectric losses major drawback decoherence but fjgures tremendously improved in the last few years Highly noise protected qubits ● Design of symmetric H suppresses low-frequency dominant noise → increase dephasing ● Subdominant sources Devoret, → spontaneuos decay Schoelkopf further limited in 3D cavity design Science 2013
artifjcial atoms artifjcial atoms mesoscopic devices with the functionality of atoms mesoscopic devices with the functionality of atoms why ? With respect to natural atoms they present ● much more fmexible design → several design solutions ● large degree of integration ● on-chip tunability ● stronger couplings → faster processing ● easy signal production and detection ● photons easily confjned in 1D fj fjg. from Xiang et al.RMP 2013 major drawback decoherence Devoret, but fjgures tremendously Schoelkopf Science 2013 improved in the last few years However combining advantages is not trivial tradeof protection ↔ available control Devoret, Schoelkopf paradigmatic example: the Lambda network Science 2013
why multilevel coherence in artifjcal atoms ? why multilevel coherence in artifjcal atoms ? at the heart of QM: interference and control of individual systems at the heart of QM: interference and control of individual systems Stokes in atomic physics ↔ interference efgects in Λ Pump network ● Coherent Population Trapping ● EIT, Autler Townes etc. C. Cohen-Tannjoudi, Kosmos Revue 2009 Scully and Zubairy, Quantum Optics 1997 individual atoms (EIT, STIRAP) Bergmann Theuer Shore, RMP 1998 Mücke et al., Nature 2010 ● controlling light with light in solid-state “artifjcial atoms” Li et al, Sci. Rep. 2012 ● AT, EIT , quantum switch, Lasing & Cooling Review You-Nori,Nature 2011 K. Bergmann motivation – advanced control tools for q-networks & fault tolerant architectures perspective – highly integrated q-networks available → new applications/efects Q-control & Q-optics in the solid state ● not a mere translation of q-optics: new elements come into play → 2+1 STIRAP ● new physical regimes/phenomena in sold-state → ultrastrong coupling
Λ Λ scheme, CPT and STIRAP scheme, CPT and STIRAP coherent population trapping → stimulated Raman adiabatic passage coherent population trapping → stimulated Raman adiabatic passage technical tool: 3-LS RWA Hamiltonian Vitanov et al., Adv. in At. Mol. and Opt. Phys. 2001 ● Stokes and Pump external AC driving fjelds ● parameters: Rabi frequencies and detunings ● two-photon detuning @ two-photon resonance → Dark state Population coherently trapped in lowest doublet Counterintuitive sequence (fjrst Stokes then pump) STIRAP adiabatic following of the dark state yields complete population transfer while remains always unoccupied Bergmann Theuer Shore, RMP 1998 Vitanov et al., Adv. in At. Mol. and Opt. Phys. 2001
few remarks on STIRAP few remarks on STIRAP Coherence guarantees robustness against imperfections in the control several 3-level interference phenomena involved Sensitivity to two-photon detunig Involves absorption-emission cycles → building block for processing in complex solid-state architectures I. Stokes V. pump STIRAP benchmark for multilevel control III.Adiabatic induced induced passage IV.pump AT phase II.Stokes In artifjcal atoms AT phase induced induced EIT phase EIT phase Vitanov et al., Adv. in At. Mol. Opt. Phys. 2001
Λ-STIRAP in artifjcial atoms ? ? Λ-STIRAP in artifjcial atoms Λ-STIRAP not yet observed in artifjcial atoms fundamental reason ● large decoherence times reqire protection Bylander et al., Net. Phys. 2011 against low-frequency noise Paladino, Galperin, Falci, Altshuler, RMP 2014 → design a device Hamiltonian with ● symmetry symmetries and work at symmetry point. point Vion et al., Science 2002; Paladino et al., RMP 2014 ● ↔ selection rules limiting the control ● in superconducting artifjcial atoms parity symmetry cancels pump fjeld Falci et al., PRB 2103. Liu et al., PRL 2005; Siewert Brandes Falci, Opt. Comm. 2006; You-Nori, Nature 2011; Falci et al., PRB 2103 same physics for devices where symmetries hold approximately
Λ-STIRAP not yet observed in artifjcial atoms STIRAP not yet observed in artifjcial atoms Λ- possible ways out possible ways out Quadratic Linear breaking (parity) symmetry Liu et al., PRL 2005; Siewert, Brandes, Falci, Opt. Comm. 2006 & PRB 2009; You-Nori, Nature 2011; Low-frequency noise optimal breaking of (parity) symmetry ● tradeof between coupling and low-frequency low+high noise → ~ 70% efciency frequency noise ● major drawback is low-frequency noise in the trapped subspace Falci et al., PRB 2103 Cooper pair box (Quantronium) pump2 symmetry st. bias point δ “2+1” Lambda scheme operated at symmetry 2 ● Good in principle but known to yield poor efcency pump1 ● Combine with advanced control allows to operate with ~100% effjciency in high-quality devices keeping high protection against low-frequency noise. Falci et al., Phys. Scr. 2102 Di Stefano et al., preprint 2015
2+1 Λ- Λ-STIRAP STIRAP 2+1 pump2 st. δ 2 pump1 Falci et al., Phys. Scr. 2102 Di Stefano et al., preprint 2015
2+1 Λ-STIRAP efective Hamiltonian STIRAP efective Hamiltonian 2+1 Λ- selection rules ← for slowly varying Goal: fjnd equivalent to of Λ scheme, ● Take efective resonance..................................... ● Take slightly detuned pump frequencies ...... → ensuring the dispersive regime................. Efgective Hamiltonian (by Magnus expansion with quasi-resonant terms only ) with same structure of desired efective two-photon pump dynamical Stark shifts
2+1 Λ-STIRAP STIRAP 2+1 Λ- two-photon pump induced Stark shift two-photon pump induced Stark shift the two-photon pump-induced Stark shifts yield a stray two-photon detuning spoiling STIRAP suitable phase modulated control cancels the efect of dynamically induced shifts yielding 100% recovery of the effjciency Phase modulation is slowly varying e.g. and easily implemented in the microwave domain
2+1 STIRAP in highly anharmonic qutrits 2+1 STIRAP in highly anharmonic qutrits fmux-based superconducting artifjcial atoms fmux-based superconducting artifjcial atoms Bylander et al., Net. Phys. 2011 6-level simulation → no leakage Includes efects of decoherence ● High-freq. noise by Lindblad eqs. → few percent loss ● Low-freq. noise in quasistatic approx. → irrelevant Large transfer effjciency can be demonstrated in in high quality devices remarkable agreement with 3-level efective H by Magnus expansion. Applications to Q-networks requiring larger fjeld strength Bloch-Siegert shifts compensated → by the same recipe
2+1 STIRAP in ~ harmonic qutrits 2+1 STIRAP in ~ harmonic qutrits superconducting artifjcial atoms in transmon design superconducting artifjcial atoms in transmon design From Xiang et al., RMP 2013 design yielding the largest decoherence times so far: up to decay-limited small anharmonicity → ofg-resonant terms of the pump drives become relevant for the efective Hamiltonian saturating efective two-photon pump dynamical Stark shift of splitting ij due to pump fjeld k
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